Renormalization of the Mean-Field Superconducting Penetration Depth in Epitaxial Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ Films

The $a-b$-plane penetration depth $\lambda \mathrm{}\left(T\right)\mathrm{}$ in Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ films, determined from kinetic inductance measurements, follows the temperature dependence of weak-coupling mean-field BCS theory near $T_c$ to within ∼0.5 K of $T_c$, resolution limited either by homogeneity or for the thinnest films by phase fluctuations. The Kosterliz-Thouless transition in a thin film is the first observation in a clean type-II superconductor, noted by the universal superfluid jump and the algebraic-decay law with a square-root cusp exponent.